The material browser manages all materials used in the scene. You can use it to add, delete or find materials. Most of the functionality of the material browser is available through it's context menu( CRTL + Click).
Delete Materials
To delete a material select the material in the material browser and press the delete key (<- ).
Find materials
The material browser offers the possibility to search for material names or material types. For example if you enter "Wood" in the upper right search field. Only those materials will be displayed which are either a wood shader or which contain the word "wood" in their name.
Save material
Once you've created a nice new material you might want to save it to the materials library for later re-usage. To do that just make a right mouse click on the material you want to save and select the "Save Material" menu command from the context menu. Now you can save the material to the material library.